Dynamic Behaviors Of The Initial Boundary Value Problem For Hyperbolic MEMS Equation

In this thesis we consider the problems of global existence, quenching behavior and viscosity dominated limit for the solutions to the local or nonlocal hyperbolic type of MEMS equationThe introduction to these problems is given in chapter1.In chapter2, we study the dynamic behavior of the solution to the local hyperbolic of MEMS equation. Firstly, since the stability of the minimal steady state, we prove that there exists a critical threshold which is the pull-in voltage λ*such that the solution exists globally in the neighborhood of the minimal steady state with exponentially convergent to this stationary if λ<λ*; while λ>λ*the solution quenches in finite time. Later, via the singular perturbation theory, we consider εâ†'0in one dimensional case and get the asymptotic behavior that the solution to (1) tends to the parabolic type ε=0.In chapter3, we study the local existence and global existence for the small initial data to the nonlocal hyperbolic MEMS equation. Using the method of the semigroup of operators, we prove the local existence; and also get the global existence if λ and the initial data are small enough.In chapter4, we consider the stability and quenching criterions to the nonlocal hyperbolic MEMS equation. We get that the solution exists globally and exponentially converges to the steady state if λ is small enough and the initial data approach this steady state. Later we also get two different quenching criterions via the functional method if λ is big enough.